The former Real Madrid head coach was appointed by the Italian club on Wednesday evening – and he is already looking at bolstering his attacking options ahead of a potential Serie A title challenge next season.
Reports in Spain claim that Ancelotti has been given a firm backing from chairman Aurelio di Laurentiis to make a move for the Frenchman, who could leave the Santiago Bernabeu.
Napoli finished second behind Juventus this season, but they pushed the league winners until the end in a competitive season.
Ancelotti and Benzema have worked together previously and it could be of the thought that Madrid president Florentino Perez could be tempted to allow him to leave.
Benzema has struggled at times for form this season, leading to calls for him to be sold – whilst he was left out of his country’s World Cup squad for previous off-field incidents.
A move to Italian football would be similar to that of Argentine striker Gonzalo Higuain, who has enjoyed success with Juventus.
Benzema’s potential exit from Madrid would leave Zinedine Zidane with a gap in his attack, relying on the likes of Cristiano Ronaldo and Gareth Bale to score goals.